Step 1: Season the chicken pieces generously with salt and pepper.
Step 2: Heat olive oil and 1 tbsp butter (or ghee) in a large skillet or cast-iron pan over medium-high heat. Once hot, add the chicken in a single layer, ensuring not to overcrowd the pan. Cook for 3-4 minutes per side until nicely browned. Remove chicken from the skillet and set aside.
Step 3: Reduce heat to medium. Add the remaining 1 tbsp butter (and 1 tbsp ghee, if using) to the skillet. Add the diced onion and cook for 3-5 minutes until softened and translucent.
Step 4: Stir in the minced garlic and grated ginger. Cook for another minute until fragrant, being careful not to burn the garlic.
Step 5: Add the garam masala, turmeric, chili powder, and cumin. Cook for 30 seconds, stirring constantly, to bloom the spices.
Step 6: Stir in the tomato paste and cook for 1 minute, stirring well to coat the aromatics.
Step 7: Pour in the chicken broth, scraping any browned bits from the bottom of the pan with a wooden spoon. Bring to a gentle simmer and cook for 2 minutes to reduce slightly.
Step 8: Reduce heat to low. Stir in the heavy cream until fully incorporated. Return the cooked chicken to the skillet, stirring to coat with the sauce.
Step 9: Let it simmer gently for 5 minutes, or until the chicken is heated through and the sauce has slightly thickened. Taste and adjust seasoning with salt, pepper, and lime juice as needed.
Step 10: Garnish with fresh chopped cilantro and serve immediately with your favorite sides like rice or naan.